7. Simplify the following using the algebra of propositions. Show your solutions. a) A = {[QV (P ^ Q)] ^ [P ^ (P ^ Q)]} b) B = {[¬(P ^ S)V ¬Q] ^ (P V ¬Q) ^ ¬(P ^ S)} c) C = [¬P → (P → Q)] → [Q → (P → P)] d) X = [(PV¬Q) A(QV¬S) ASA¬(PAQ AS)]

Q: 8. Construct the truth table for the following propositions: a. (pv q)^r] →P b. (pr) → (gr) c. [pv…

A: As per our guideline, we are supposed to solve only first three subparts. Kindly repost other…

Q: 7. Simplify the following using the algebra of propositions. Show your solutions. a) A = {[QV (P^Q)]…

A: Solution a: Given A≡¬Q∨(P∧Q∧P∧(P∧Q) We can write it as A≡¬Q∨(P∧Q∧P∧P∧Q Using Idempotent law P∧P=P So…

Q: Use the laws of propositional logic to prove that the following compound propositions are…

A:

Q: Evaluate (p → q) ^ (¬p → q) = O pnq O p-q O p

A:

Q: Use inference rules and laws of propositional logic to infer 3x(R(x) ^ ¬T(x)) from the following…

A:

Q: (b) (p^¬q) → r = r → (pVq).

A:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Find their truth values of the following propositions, using…

A:

Q: 3. Consider the following propositions: P→ 9. g^-P. -P→→q, -pvq, 9 → P. -q V p. -9→P. P^-4. (a)…

A:

Q: [(A ^¬B) → C] (¬C→ ¬D) b. ¬[(A → B) → C]V ¬ {[A→(B ^ C)1→¬D}

A:

Q: c) not a tautology. pV ¬q (pV ¬q) → q True True False True True True False True True False False…

A:

Q: Show via a sequence of justified logical equivalences that p→ (qr) is logically equivalent to (p^q)…

A: Answer :-  We have to draw the truth table to check the logical equivalence of both statements.

Q: ((p v q) → ¬a) = O (a → (-qa-p)) O (a → (-qvp) O (a → (qn-p) O (a → (-qv-p))

A:

Q: 1. Show that (-p^q)^(q>p) is a contradictory using replacement rules and truth table

A:

Q: Write out the negations of the following propositions: (a) (3m) ((m<8) ^ (m ≥ 2)).

A:

Q: Show that (p →q) and p ^-q are logically equivalent.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Evaluate (p v q v -r) ^ (p v ¬q v ¬s) ^ (p v ¬r v ¬s) ^ (¬p v ¬q v ¬s) ^ (p v q v ¬s). O…

A:

Q: What is the truth value of the compound proposition if p and q are true statements and r and s are…

A:

Q: Which of the following is a valid equivalency for ¬(p^q) according to the laws of propositional…

A: We know Demorgon's Law  ¬(p∨q)≡¬p∧¬q  and ¬(p∧q)≡¬p∨¬q Hence for the given questions   ¬(p∧q)≡¬p∨¬q

Q: D. Determine the truth value of each proposition. 1. (p^q) →~ (q-p) 2. (pq) → [(p→q) ^ (q v~q)]

A:

Q: (А — (В — с)) — (в — (4 — с)) с.

A:

Q: Q6. Let P, Q, and R be any three statements given below. (PA~Q) v [P A~(Q V R)] v [Q ^ ~(Q v R)]…

A:

Q: PART 1: Logical Equivalence Direction: Use truth tables to verify these logical equivalences 1.…

A: The logical equivalences are: 1. p∧q⇔p≅p⇒q 2. p∧q⇒r≅p⇒¬q∨r 3. p⇒¬q∧p⇒¬r≅¬p∧q∨r 4. p⇒q∧r≅p⇒q∧p⇒r To…

Q: Use propositional logic, rules of inference to prove that the following arguments are valid: (A →…

A:

Q: a) Use Laws of logic to simplify following statement. -(-(p^q) → q)

A:

Q: Determine whether (p→g) ^ (p Vr) and -p V (q^r) are two logically equivalent propositions.

A: Given that               (p→q)∧(¬p∨r)¬p∨(q∧r) Here we need to prove both logics are equivalent. For…

Q: 5. Find the truth tables for (a) (P V (¬Q)) v (Q ^ (¬P)), and (b) (P = (¬Q)) ^ (Q → (¬P)).

A: (a)   We need to find truth table for  (P ∨ (¬Q)) ∨ (Q ∧ (¬P)). We know that a conjunction (∧) is…

Q: 5) Let the domain of discourse be the set of real numbers. Indicate which propositions are true and…

A:

Q: 3. Which of the following pairs of propositional forms are equivalent? (a) ~(P AQ),(~P)^(~Q). (b) P⇒…

A:

Q: Use propositional logic, rules of inference to prove that the following arguments are valid: (A →…

A:

Q: b. (p^q) v (( ¬p) → q) V C. - (p^ (qvp) ) → p

A: Here ,we have to find truth tables for sub-parts b, c.

Q: e. 8 b(dv(b←d)) (d~←b_)↔(b←d) ' (bnd)v(b_vd)

A:

Q: (~a v b)^{[c → (d → ~c)]^~b} A В T F

A: We will find out the required truth table.

Q: 3. Use algebra of propositions to show that (p ^ q) V (p^~q) → p

A: p∧q∨p∧~q↔p